##
##  i n t e r v a l . R  Interval Functions
##


interv_union <- function(M) {
    if (is.null(M)) return(c())
    if (is.vector(M)) {
        if (length(M) %% 2 == 0) M <- as.matrix(M, ncol = 2)
        else stop("Length of 'M' must be an even number.")
    }
    if (!is.numeric(M) || !is.matrix(M) || ncol(M) != 2)
        stop("Argument 'M' must be a matrix with two columns.")
    if (nrow(M) == 1) return(c(M))
    if (any(M[, 1] > M[, 2]))
       stop("Left endpoint cannot be larger than right endpoint.")
    
    o <- order(c(M[, 1], M[, 2]))
    n <- cumsum( rep(c(1, -1), each=nrow(M))[o])
    startPos <- c(TRUE,  n[-1] == 1 & n[-length(n)] == 0)
    endPos   <- c(FALSE, n[-1] == 0 & n[-length(n)] == 1)
    M <- M[o]
    cbind(M[startPos], M[endPos])
}

#   o <- order(M[, 1], M[, 2])
#   L <- M[o, 1]; R <- M[o, 2]
#   k <- 1
#   Mnew <- matrix(c(L[k], R[k]), 1, 2)
#   for (i in 2:nrow(M)) {
#       if (L[i] <= Mnew[k, 2]) {
#           Mnew[k, 2] <- max(R[i], Mnew[k, 2])
#       } else {
#           k <- k+1
#           Mnew <- rbind(Mnew, c(L[i], R[i]))
#       }
#   }
#   return(Mnew)


interv_intersect <- function(M) {
    if (is.null(M)) return(c())
    if (is.vector(M)) {
        if (length(M) %% 2 == 0) M <- as.matrix(M, ncol = 2)
        else stop("Length of 'M' must be an even number.")
    }
    if (!is.numeric(M) || !is.matrix(M) || ncol(M) != 2)
        stop("Argument 'M' must be a matrix with two columns.")
    if (any(M[, 1] > M[, 2]))
        stop("Left endpoint cannot be larger than right endpoint.")
    if (nrow(M) == 1) return(c(M))

    L <- max(M[, 1]); R <- min(M[, 2])
    return(if (L <= R) c(L, R) else c())
}